Tag: Perfect

c# – Unity, Pixel Perfect and Scaling

I am totally stuck on with pixel perfectness of the game. I have tried a few pixel perfect camera -assets, but they have lots of issues considering scalability. is it normal that these cameras zoom in and out, instead of scaling the camera screen when using different resolutions for the game. Because this is a huge problem for me, cause i need to make a game for aspect ratio of 16:10, and every resolution that has the same aspect ratio is needed to scale it correctly keeping the pixel perfectness. The ortographic camera size is dependent of screen width (width / PPU / 2) So it always zooms in or out with different resolutions.

Question is: Is there a way to make it scale the game sprites instead of zooming the view?

reference request – Jacobson-style Galois theory on perfect closure

Jacobson developed a ‘Galois’ correspondence for purely inseperable extensions of exponent 1 (only consisting of pth roots), where he showed there was a correspondence between its subfields and lie-algebras of derivations given below:
$$Fmapsto mathcal{D}_F(K)$$
$$mathcal{D’}mapsto F, text{the field of constants of} space mathcal{D’}$$
Davis extends this to exponent 2 extensions, and conjectures that higher derivation Lie-algebras should correspond to higher exponents.
Firstly, I’d like to ask for a list of books or articles that explore these ideas, especially the research done in 1968-1975 or more recently. I found the original papers in the American Mathematical Society very inaccessible, and have mostly been working of Lindsay Childs’ survey of this research, but would like to learn more.

The other question I have, is if this theory is applicable to the perfect closure of a field (in its algebraic closure, or more generally): is there a corresponding notion of an ‘absolute lie-algebra of derivations’ to that of the absolute galois group? If so please provide me with references to this too.

upper lower bounds – Is this a valid proof for $I(n^2) geq frac{5}{3}$, if $q^k n^2$ is an odd perfect number with special prime $q$?

Let $sigma(x)$ denote the sum of divisors of the positive integer $x$, and let $I(x)=sigma(x)/x$ be the abundancy index of $x$.

Note that both $sigma$ and $I$ are multiplicative functions.

A number $m$ is said to be perfect if $sigma(m)=2m$. Equivalently, $I(m)=2$.

Euler proved that an odd perfect number, if one exists, must have the form
$$m = q^k n^2$$
where $q$ is the special prime satisfying $q equiv k equiv 1 pmod 4$ and $gcd(q,n)=1$.

Since $q$ is prime, we have
$$frac{q+1}{q} = I(q) leq I(q^k) = frac{sigma(q^k)}{q^k} = frac{q^{k+1} – 1}{q^k (q – 1)} < frac{q^{k+1}}{q^k (q – 1)} = frac{q}{q – 1}$$
from which it follows that
$$frac{2(q-1)}{q} < I(n^2) = frac{2}{I(q^k)} leq frac{2q}{q+1}.$$

Note that we then have the lower bound
$$I(n^2) > frac{2(q-1)}{q} geq frac{8}{5}$$
since $q$ is a prime satisfying $q equiv 1 pmod 4$.

Here is my initial question:

Can we improve the lower bound for $I(n^2)$ to
$$I(n^2) geq frac{5}{3}$$
using the following argument?

$$bigg(frac{2q}{q+1} geq I(n^2) > frac{5}{3}bigg) implies q > 5 implies q geq 13 implies bigg(I(n^2) > frac{2(q-1)}{q} geq frac{24}{13} > frac{5}{3}bigg)$$

Thus, we have the biconditional
$$I(n^2) > frac{5}{3} iff q > 5.$$

Next, we have the implication
$$I(n^2) = frac{5}{3} implies q = 5.$$

It then suffices to prove the implication
$$q = 5 implies I(n^2) = frac{5}{3}$$
to finally show that
$$I(n^2) geq frac{5}{3},$$
since $q geq 5$ holds.

But note that, if $q=5$, then
$$frac{5}{3} = I(n^2) = frac{2}{I(5^k)} = frac{2cdot{5^k}(5-1)}{5^{k+1}-1}$$
which implies that the Descartes-Frenicle-Sorli Conjecture that $k=1$ holds.

Still, notice that we have
$$k=1 implies I(q^k) = I(q) = frac{q+1}{q} = 1 + frac{1}{q} leq frac{6}{5} implies I(n^2) = frac{2}{I(q^k)} = frac{2}{I(q)} geq frac{2cdot{5}}{6} = frac{5}{3},$$
which is what we set out to prove.

Here is my final question:

Would it be possible to remove the reliance of the proof on the Descartes-Frenicle-Sorli Conjecture?

I will be your virtual assistant for perfect data entry and web research for $5

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I will provide perfect 1000 to 2000 words Content Writing and Article writing to your Blog for $10

I will provide perfect 1000 to 2000 words Content Writing and Article writing to your Blog

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Bridal Pearl Jewelry – Choosing Perfect Pearl Wedding Jewelry – Newbies Lounge

Are you looking for something that will make you most beautiful on your wedding? Then you have to choose for Bridal Pearl Jewelry that will be something enchanting and will give you glamorous look to you. Bridal Peal Jewelry adds elegance and high degree of tradition to the total appearance of the bride.

Pearls are the only precious gems that are created by living creature. Pearl wedding jewelry is a good accent of classic tradition and it is believed that pearl brings prosperity and good fortune to the wedding life. Wearing Pearl wedding jewelry on your wedding will not only make you feel beautiful and gorgeous, it will excel to your own personality.

Bridal pearl jewelry would be the perfect choice for the most grandiose wedding and your bridesmaid will look gorgeous with the all-natural pearl wedding jewelry set. If you are sticking with theme for your wedding occasion, then you have to go for while pearl wedding jewelry that perfectly matches your wedding gown. If you want spotlight on the bridesmaid, you have to wear Bridal pearl jewelry. Even you can wear pearls on cufflinks and neckties too. Bridal Pearl jewelry would be the perfect theme for your wedding which gives you classic tradition feel with modern looks.

However you may want to choose your bridal jewelry, you should always put in context your own individuality and personal style. Your own Wedding will make a wonderful memory you but for everyone involved in the event. Focusing on the solemnity of the ceremony should be prioritized and not just how everything should fit in. After all, it is the pronouncement of love that was made between you and your loved one.

Your bridal jewelry should be the context to your individuality and personal style. You wedding will male wonderful memory for you and your wedding attire and apparels would bring you such the beautiful memories once again. Choosing Pearl wedding jewelry would pronounce your memories well and it would bring you happy always.

How to Select Wedding Pearl Jewelry

The bridal pearl jewelry should be well matched with the bride’s attire. For example, her pearl earrings would be the same type and color as her other pearl accessories. In addition, her wedding pearl jewelryshould give her featured attraction and would make her looks good.

You have to keep in mind on the color coordination of pearls with the wedding gown. If your gown is ivory colored, you have to wear pearls of white color. The bridal pearl jewelry set should also be white. All the pearls on the bride’s attire and wedding pearl jewelry set should look like they are made to go together.

If the bride would like to wear a necklace, earrings or other pearl accessories that doesn’t match her entire attire or apparel, it is better to place a note in the program stating that the bride is wearing.

If a bride or bridesmaid wearing a necklace, it should at least an inch above the neckline would give more attraction. Make sure that the pearl wedding jewelry should reflect the quality of the entire attires and apparels. It is necessary to wear proper and perfect dress that would suits all her apparels.

Why Should I Choose Pearl Wedding Jewelry For My Wedding?

It is believed that pearls have been the synonyms with purity, sophistication and romance. Pearl wedding jewelry will bring you classic tradition look and make the bride look gorgeous with dazzling white pearls.

Pearls are all natural created by living creature. Pearls are available in variety of colors, shapes and tones. Pearls are versatile and pearl wedding jewelry would be the perfect choice that support any wedding theme.

Matching the Wedding Theme

You have to consider the overall theme of the marriage before deciding to buy bridal wedding jewelry.

Traditional

Your Pearl wedding jewelry set would be more attractive if you choose pearls of Pure white or ivory Akoya. South Sea or Freshwater pearl wedding jewelry sets are the classic choice for a traditional wedding. Larger sizes, starting in the 7-8mm range are customary.

Modern / Contemporary

If you prefer modern style of wedding, then White South Sea pearl pendant and earring sets are excellent choices

Tropical

Black Tahitian or Golden South Sea pearl sets are ideal choices for an exotic wedding.

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http://www.jewelryspecialist.biz/bridal-pearl-jewelry.html

I will do perfect data entry, web research, data collection and copy paste work for $5

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